Web search and reading web pages are available on every plan, Free included. Each web search and each page read uses part of your usage allowance, the same allowance that your chats use. There is no separate share for web search: you can spend your allowance on chats, web searches or both, as you like. Read Check your usage and what happens at a limit to see how much you have used.
When your allowance is used up
When there is no allowance left for the day or the week, Bluedeer still tries your web search once more in a way that does not use your allowance. If that works, you get your results as usual, and nothing is taken from your allowance. If it does not work, the assistant tells you that searches are not available because your usage limit is reached, and when it resets.
This works the same on every plan, Free included.
On Economy and higher plans
Economy, Pro, Premium and Max also have a daily and a weekly count for web searches. The app does not show these counts. If you reach one, the assistant tells you that the day's or the week's web search limit is reached.
The day starts over at midnight UTC, and the week on Monday at midnight UTC, the same as the rest of your usage.